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Uncertainty: Confidence Intervals

Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...

Uncertainty: Overview

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Propagation of Uncertainty from Systematic Error

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...

Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

Prediction Intervals

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.

Confidence Intervals

Confidence Intervals

An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a sample proportion. However, unlike the point estimate which is a single value, the confidence interval contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A...

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Updated: Sep 8, 2025

A Data-Driven Approach to Quantifying Immune States in Sepsis

A Data-Driven Approach to Quantifying Immune States in Sepsis

Published on: February 7, 2025

马巴时间序列预测与不确定性量化

Pedro Pessoa^1,2, Paul Campitelli^1,2, Douglas P Shepherd^1,2

¹Center for Biological Physics, Tempe, AZ, United States of America.

Machine learning: science and technology

|July 24, 2025

概括

此摘要是机器生成的。

像Mamba这样的状态空间模型对时间序列预测有希望,但缺乏准确的不确定性量化. 我们的Mamba-ProbTSF方法通过建模预测不确定性来增强Mamba,提高电力和交通数据的预测可靠性.

关键词:

时间序列预测时间序列预测非线性动力学的非线性动力学国家空间模型.不确定性量化不确定性量化

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科学领域:

机器学习机器学习
时间序列分析时间序列分析
概率学预测概率学预测

背景情况:

包括Mamba在内的状态空间模型越来越多地用于时间序列预测,因为它们具有序列模式识别能力.
现有的Mamba实现显示了电力消耗中显著的平均误差 (约. 8%) 和交通占用率 (约. 18%) 的基准指标.
需要量化Mamba预测中的不确定性,以区分不准确性和固有的数据变化.

研究的目的:

开发一种方法来量化基于Mamba的时间序列预测的预测不确定性.
引入一个双网络框架,Mamba-ProbTSF,用于使用Mamba架构进行概率预测.
与现有方法相比,评估Mamba-ProbTSF的性能和可靠性.

主要方法:

提出了一个双网络框架,集成Mamba用于概率时间序列预测.
一个网络生成点预测;第二个网络通过估计差异来模型预测不确定性.
使用概率TSF (Mamba-ProbTSF) 工具实现了Mamba,代码可在GitHub上找到.

主要成果:

实现了减少Kullback-Leibler分歧 (合成数据为10^-3,现实数据为10^-1),表明了改进的概率分布建模.
验证了真实轨迹在基准数据集中约95%的时间都处于预测的两西格玛不确定性区间内.
与DeepAR和ARIMA相比,持续显示较低的预测误差和更可靠的不确定性量化.

结论:

Mamba-ProbTSF有效量化了Mamba预测中的预测不确定性,提高了时间序列预测任务的可靠性.
该方法在DeepAR和ARIMA等领先的概率预测模型中表现出卓越的性能.
该框架有可能在随机过程中应用,包括布朗运动和分子动力学.